[Merged by Bors] - feat(normed_space/inner_product): euclidean_space.norm_eq #6744
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pechersky
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Mar 17, 2021
pechersky
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Can we try to do this by fixing the diamond? I think that's the more natural approach. |
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I'm only adding the lemma that expands out the norm for a term of the |
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Ah, I see. Can you please give this lemma for |
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| @@ -229,6 +229,11 @@ lemma norm_eq {p : ℝ} {hp : 1 ≤ p} {α : ι → Type*} | |||
| [∀i, normed_group (α i)] (f : pi_Lp p hp α) : | |||
| ∥f∥ = (∑ (i : ι), ∥f i∥ ^ p) ^ (1/p) := rfl | |||
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| lemma norm_eq_of_nat {p : ℝ} {hp : 1 ≤ p} {α : ι → Type*} | |||
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I added this lemma because of the notational confusion between ^ when encoding rpow or monoid.pow. For working with nat powers, this will allow for cleaner rewrites, with easy discharging with norm_num. I couldn't figure out how to use . tactic.norm_num as the out_param there.
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I added this lemma because of the notational confusion between
^when encodingrpowormonoid.pow. For working withnatpowers, this will allow for cleaner rewrites, with easy discharging withnorm_num. I couldn't figure out how to use. tactic.norm_numas the out_param there.
This seems reasonable to me, but I'd like someone like @sgouezel who's been involved in the design of the L^p spaces to decide about this, in case there's a reason we haven't had lemmas like this already.
Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
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bors r+ |
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Co-authored-by: Yakov Pechersky <pechersky@users.noreply.github.com>
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Co-authored-by: Yakov Pechersky <pechersky@users.noreply.github.com>
